Advertisements
Advertisements
प्रश्न
Find the smallest number by which 180 must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.
Advertisements
उत्तर
The prime factorisation of 180:
180 = 2 x 2 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we get:
180 = (2 x 2) x (3 x 3) x 5
The factor, 5 does not have a pair. Therefore, we must multiply 180 by 5 to make a perfect square. The new number is:
(2 x 2) x (3 x 3) x (5 x 5) = 900
Taking one factor from each pair on the LHS, the square root of the new number is 2 x 3 x 5, which is equal to 30.
संबंधित प्रश्न
Find the square root of the following number by the prime factorisation method.
5929
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
396
By just examining the unit digit, can you tell which of the following cannot be whole square?
1022
Write true (T) or false (F) for the following statement.
The sum of two square numbers is a square number.
Write true (T) or false (F) for the following statement.
The difference of two square numbers is a square number
Find the squares of the following numbers using column method. Verify the result by finding the square using the usual multiplication:
71
Find the square root the following by prime factorization.
196
The students of class VIII of a school donated Rs 2401 for PM's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Find the smallest perfect square divisible by 3, 4, 5 and 6.
Examine if the following is a perfect square.
841
